Medical diagnostic imaging instruments and electronic networks have resulted in accumulation and on-line availability of large collections of digital medical images, but it is recognized that there are significant scientific challenges to transforming these collections into "image databases" and that image-database appropriate software tools do not currently exist. To be useful, an image database must possess a mechanism for indexing and extracting images based on a user-defined query. While the use of textual indices may serve some purposes, the information content of images implies that indexing by textual tags would not be wholly sufficient. We propose to further develop and evaluate a framework we have devised for constructing and indexing medical image databases by conducting theoretical and experimental research on geometric database schemas, geometrical point set operators, and active image segmentation. At the center of our approach is the further development of an axiomatic, geometric analysis system that computes geometric properties of explicit and implicit point sets in medical images. By axiomatic, we mean in a domain-knowledge independent manner. In our past-supported effort we developed an early version of the geometric database schema which we termed a point set schema . The schema is general in that it can be applied to a large diverse class of medical images and consists of mathematically describing the different organs, chambers, and vessels in an image in terms of point sets that occupy the image. Tools for mathematical morphology are used to develop properties of the image from these point sets. The tools are general and do not require domain-specific knowledge. The effort of this application would focus on: 1) completing the detailed design and development of this reasoning system, including the development of specific modules for defining both explicit and implicit point sets and their features, 2) implementing the geometric reasoning modules within a software test platform, and 3) evaluating the performance of the entire geometric reasoning framework using test point sets and their features on an image database consisting of a large collection of tomographic magnetic resonance cardiac images.